Supporters and opponents of Egypt's Muslim Brotherhood are set to stage rallies across the country as they mark the first Friday of Ramadan after days of bloody violence.

Scores of supporters of deposed president Mohamed Morsi, who are already camping in Cairo, will take part in the demonstrations after the Brotherhood called on Egyptians to gather in support of its leader.

The protesters have vowed that they will continue "peaceful resistance to the bloody military coup against constitutional legitimacy".

The Brotherhood is trying to demonstrate its strength despite the detention of scores of its leaders by the army, and the massacre of 51 Morsi supporters outside the Republican Guard headquarters in Cairo.

The forces ranged against Morsi have also called for rallies in support of the uprising against the Islamist administration. These rallies are also expected to draw huge crowds.

A joint statement by the anti-Morsi groups has urged Brotherhood campaigners to "immediately stop inciting violence and terrorism against Egyptians".

It added that Egyptians should demonstrate to make sure that "the will of the people is expressed in the transitional phase so as to correct the path of the 25 January revolution".

Meanwhile, the US has warned the interim administration over "arbitrary" arrests of senior Brotherhood figures.

"You're working against yourself if your effort is to be inclusive. The only way this is going to work successfully... is if all parties are encouraged and allowed to participate and that's why we've made clear that arbitrary arrests are not anything that we can support," said White House spokesperson Jay Carney.

The UN chief has also expressed similar concern. "There is no place for retribution or for the exclusion of any major party of community in Egypt," Ban Ki-moon is quoted as saying during a telephone conversation with Egyptian Foreign Minister Kamel Amr.